Abstract

Visualisation of complex nonlinear equation solutions is a useful analysis tool for various scientific and engineering applications. We have re-examined the geometrical interpretation of the classical nonlinear four-wave mixing equations for the specific scheme of a phase sensitive one-pump fiber optical parametric amplification, which has recently attracted revived interest in the optical communications due to potential low noise properties of such amplifiers. Analysis of the phase portraits of the corresponding dynamical systems provide valuable additional insight into field dynamics and properties of the amplifiers. Simple geometric approach has been proposed to describe evolution of the waves, involved in phase-sensitive fiber optical parametric amplification (PS-FOPA) process, using a Hamiltonian structure of the governing equations. We have demonstrated how the proposed approach can be applied to the optimization problems arising in the design of the specific PS-FOPA scheme. The method considered here is rather general and can be used in various applications.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  5. C. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (1)

2015 (4)

2013 (1)

J. R. Ott, H. Steffensen, K. Rottwitt, and C. J. McKinstrie, “Geometric interpretation of four-wave mixing,” Phys. Rev. A 88, 043805 (2013).
[Crossref]

2011 (3)

H. Steffensen, J. R. Ott, K. Rottwitt, and C. J. McKinstrie, “Full and semi-analytic analyses of two-pump parametric amplification with pump depletion,” Opt. Express 19, 6648–6656 (2011).
[Crossref] [PubMed]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

2010 (1)

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

2008 (1)

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
[Crossref]

2007 (1)

C. J. McKinstrie, S. Radic, and A. H. Gnauck, “All-optical signal processing by fiber-based parametric devices,” Opt. Photonics News 18, 34–40 (2007).
[Crossref]

2004 (1)

2003 (1)

S. Radic and C. J. McKinstrie, “Two-pump fiber parametric amplifiers,” Opt. Fiber Technol. 9, 7–23 (2003).
[Crossref]

2002 (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Topics Quantum Electron. 8, 506–520 (2002).
[Crossref]

1991 (1)

1975 (1)

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11, 100–103 (1975).
[Crossref]

Andrekson, P. A.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photonics Rev. 9, 50–74 (2015).
[Crossref]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Topics Quantum Electron. 8, 506–520 (2002).
[Crossref]

Bendahmane, A.

Blessing, D. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Bogris, A.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Cappellini, G.

Conforti, M.

Dasgupta, S.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Doran, N. J.

Ellis, A. D.

A. Perentos, S. Fabbri, M. Sorokina, I. D. Phillips, S. K. Turitsyn, A. D. Ellis, and S. Sygletos, “QPSK 3R regenerator using a phase sensitive amplifier,” Opt. Express 24, 16649–16658 (2016).
[Crossref] [PubMed]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Fabbri, S.

Futami, F.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
[Crossref]

Gnauck, A. H.

C. J. McKinstrie, S. Radic, and A. H. Gnauck, “All-optical signal processing by fiber-based parametric devices,” Opt. Photonics News 18, 34–40 (2007).
[Crossref]

Gruner-Nielsen, L.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

Grüner-Nielsen, L.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Topics Quantum Electron. 8, 506–520 (2002).
[Crossref]

Harper, P.

Hedekvist, P. O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Topics Quantum Electron. 8, 506–520 (2002).
[Crossref]

Herstrom, S.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Huettl, B.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
[Crossref]

Jakobsen, D.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Jazayerifar, M.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photonics Rev. 9, 50–74 (2015).
[Crossref]

Kakande, J.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Karlsson, M.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Kudlinski, A.

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Topics Quantum Electron. 8, 506–520 (2002).
[Crossref]

Ludwig, R.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
[Crossref]

Lundström, C.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Marhic, M. E.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photonics Rev. 9, 50–74 (2015).
[Crossref]

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2008).

McKinstrie, C.

McKinstrie, C. J.

J. R. Ott, H. Steffensen, K. Rottwitt, and C. J. McKinstrie, “Geometric interpretation of four-wave mixing,” Phys. Rev. A 88, 043805 (2013).
[Crossref]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

H. Steffensen, J. R. Ott, K. Rottwitt, and C. J. McKinstrie, “Full and semi-analytic analyses of two-pump parametric amplification with pump depletion,” Opt. Express 19, 6648–6656 (2011).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and A. H. Gnauck, “All-optical signal processing by fiber-based parametric devices,” Opt. Photonics News 18, 34–40 (2007).
[Crossref]

S. Radic and C. J. McKinstrie, “Two-pump fiber parametric amplifiers,” Opt. Fiber Technol. 9, 7–23 (2003).
[Crossref]

Mussot, A.

O’Gorman, J.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Okabe, R.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
[Crossref]

Ott, J. R.

Parmigiani, F.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Perentos, A.

Petropoulos, P.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photonics Rev. 9, 50–74 (2015).
[Crossref]

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Peucheret, C.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photonics Rev. 9, 50–74 (2015).
[Crossref]

Phelan, R.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Phillips, I. D.

Puttnam, B. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Radic, S.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photonics Rev. 9, 50–74 (2015).
[Crossref]

C. J. McKinstrie, S. Radic, and A. H. Gnauck, “All-optical signal processing by fiber-based parametric devices,” Opt. Photonics News 18, 34–40 (2007).
[Crossref]

C. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
[Crossref] [PubMed]

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J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
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Rottwitt, K.

Schmidt-Langhorst, C.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
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Schubert, C.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
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Sjödin, M.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
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Slavik, R.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
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R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
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Syvridis, D.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
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Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
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Toda, H.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
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Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
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Turitsyn, S. K.

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S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
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S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
[Crossref]

Weerasuriya, R.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
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Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Topics Quantum Electron. 8, 506–520 (2002).
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IEEE J. Quantum Electron. (1)

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11, 100–103 (1975).
[Crossref]

IEEE J. Sel. Topics Quantum Electron. (2)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Topics Quantum Electron. 8, 506–520 (2002).
[Crossref]

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An Optical Parametric Amplified Fiber Switch for Optical Signal Processing and Regeneration,” IEEE J. Sel. Topics Quantum Electron. 14, 674–680 (2008).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photonics Rev. 9, 50–74 (2015).
[Crossref]

Nat. Photonics (3)

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
[Crossref]

Opt. Express (6)

Opt. Fiber Technol. (1)

S. Radic and C. J. McKinstrie, “Two-pump fiber parametric amplifiers,” Opt. Fiber Technol. 9, 7–23 (2003).
[Crossref]

Opt. Photonics News (1)

C. J. McKinstrie, S. Radic, and A. H. Gnauck, “All-optical signal processing by fiber-based parametric devices,” Opt. Photonics News 18, 34–40 (2007).
[Crossref]

Phys. Rev. A (1)

J. R. Ott, H. Steffensen, K. Rottwitt, and C. J. McKinstrie, “Geometric interpretation of four-wave mixing,” Phys. Rev. A 88, 043805 (2013).
[Crossref]

Other (1)

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2008).

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Figures (5)

Fig. 1
Fig. 1 Phase portraits: k = 2 (left), k = −0.5 (middle), k = −2 (right).
Fig. 2
Fig. 2 (a) Phase portrait for k = −0.7. (b) Schematic depiction of the power transfer process in PS-FOPA with a fixed gain.
Fig. 3
Fig. 3 Evolution of the pump power (solid red), signal (idler) power (solid green) and relative phase θ (dashed blue) during two full periods of the 1st type trajectory.
Fig. 4
Fig. 4 (a) Dependence of PS-FOPA length on initial relative phase θ(0) for G = 40 (green), 45 (blue) and 50 (red) dB. (b) Dependence of G on PS-FOPA length for θ(0) = 0 (solid red), 0.8 (dashed red) and 3 (solid black) rad. P1 = 3 W, P2 = P3 = 0.01 mW.
Fig. 5
Fig. 5 Dependence of G on PS-FOPA length and pump power. θ(0) = 0, P2 = P3 = 0.01 mW.

Equations (24)

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d P 1 d Z = 2 d P 2 d Z = 2 d P 3 d Z = 4 P 1 P 2 P 3 sin θ ,
d θ d Z = Δ β γ + ( 2 P 1 P 2 P 3 ) + P 1 P 2 P 3 ( P 2 1 + P 3 1 4 P 1 1 ) cos θ ,
δ p = P 2 P 3 ,
P T = P 1 + P 2 + P 3 .
d P 1 d Z = 2 P 2 d Z = 4 P 1 P 2 sin θ ,
d θ d Z = Δ β γ + 2 ( P 1 P 2 ) + P 1 P 2 ( 2 P 2 1 4 P 1 1 ) cos θ = = Δ β γ + 2 ( P 1 P 2 ) + ( 2 P 1 4 P 2 ) cos θ .
d P 1 d Z = H θ = 2 P 1 ( P T P 1 ) sin θ ,
d θ d Z = H P 1 = 2 ( 2 P 1 P T ) cos θ + 3 P 1 P T + Δ β γ .
H = 2 P 1 ( P T P 1 ) cos θ 3 2 P 1 2 + ( P T Δ β γ ) P 1 .
H = 2 p ( 1 p ) cos θ 3 2 p 2 + ( 1 k ) p ,
d p d l = H θ = 2 p ( 1 p ) sin θ ,
d θ d l = H p = ( k 1 ) + 3 p 2 ( 1 2 p ) cos θ ,
p A = 0 , p B = 1 , θ C = 2 π n , θ D = 2 π n + π , n Z .
cos θ A = k 1 2 , cos θ B = k + 2 2 , p C = 3 k 7 , p D = k + 1 .
H = 2 p ( 1 p ) cos θ 3 2 p 2 + ( 1 k ) p ,
d p d l = 2 p ( 1 p ) sin θ .
cos θ = H + 3 2 p 2 ( 1 k ) p 2 p ( 1 p ) .
α ( H , p ) = sin θ = ± 1 cos 2 θ .
d p 2 p ( 1 p ) α ( H , p ) = d l ,
p ( 0 ) p ( L ) d p 2 p ( 1 p ) α ( H , p ) = 0 L d l L .
H ˜ ( p , θ ) = H ( p , θ ) + k + 1 / 2 = 1 2 ( 1 p ) ( ( 4 cos θ + 3 ) p + 2 k + 1 ) .
p = 2 k + 1 4 cos θ + 3 .
d θ d l + 2 cos θ + 2 + k = 0 ,
d θ ( 2 cos θ + 2 + k ) = d l .

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